Calibration results from my WSKO-BGA: actual apex angle vs. tool setting

[cbwx34]

Cool. I can't see the scale... if I zoom in, it's just a blur. I suspect (theorize?) that such a small section may be part of the reason for the difference here.

 

[Cyrano]

Cool. I can't see the scale... if I zoom in, it's just a blur.

No, of course you can't. I apologize; I thought I'd posted some images with a legible scale.

I suspect (theorize?) that such a small section may be part of the reason for the difference here.

I've thought the same. However, your results with the Sharpie don't seem to support this.

 

[cbwx34]

I actually think that might be the reason for the difference. Even the Sharpie testing might not pick up a change in such a small area, and even if it did, it could be easily compensated for, without even realizing. Have to give that some thought.

 

[Cyrano]

I actually think that might be the reason for the difference. Even the Sharpie testing might not pick up a change in such a small area, and even if it did, it could be easily compensated for, without even realizing. Have to give that some thought.

Theory proposes, experiment disposes. I'm eager to get your samples. so that I can get this corn out from between my teeth.

 

[cbwx34]

Hahaha. Ok. Reason I bring this up though... it makes me wonder if the testing itself is the issue? I think a simple sharpener comparison, if you have one (similar to what I did)... would answer a lot of this?

 

[David45]

Where does one measure the angle along a convex curve?

Update
I found a 2013 thread but don’t know how to link it here.

 

[Cyrano]

Theory proposes, experiment disposes. Let's start with theory:

Consider a thin blade having an edge apex angle of 37 degrees inclusive being sharpened in the WSKO-BGA. The blade is kept horizontal at 0 degrees, and the tool is set to a belt angle of 10 degrees, with the intent of achieving a new blade apex angle of 20 degrees inclusive.

Start with no contact between the blade and the belt:

Now bring the blade towards the belt, keeping the blade at 0 degrees, until the blade just contacts the belt. Contact will be made at the shoulder of the existing edge:

As the blade is pushed against the belt, the belt begins to flex:

As sharpening proceeds, steel is removed from the blade, and the sharpened region gets wider. This continues until the sharpened region hits the apex:

The blade is flipped over, and the sharpening process is repeated on the other side:

The final edge geometry has an angle of 15 degrees inclusive at the edge shoulder, and 24 degrees inclusive at the apex. The inclusive apex angle is 4 degrees greater than the intended target.

Now let's repeat this exercise for a thicker blade, with the same initial edge apex profile, and keeping the same 10-degree setting for the tool.

Start with no contact between the blade and the belt:

Now bring the blade towards the belt, keeping the blade at 0 degrees, until the blade just contacts the belt. Contact will be made at the shoulder of the existing edge:

As the blade is pushed against the belt, the belt begins to flex:

As sharpening proceeds, steel is removed from the blade, and the sharpened region gets wider. This continues until the sharpened region hits the apex:

The blade is flipped over, and the sharpening process is repeated on the other side:

The final edge geometry has an angle of 17 degrees inclusive at the edge shoulder, and 37 degrees inclusive at the apex. The inclusive apex angle is 17 degrees greater than the intended target.

So much for theory. Now, experiment disposes:

This sample shows my sharpening results for an Opinel no. 8, made from thin blade stock (0.07 inches thick.) The WSKO-BGA was set to 15 degrees, so we should expect a nominal edge angle of 30 degrees:

For this thin blade, the offset between the tool setting and what I measure as the inclusive apex angle is 3 degrees.

This sample shows my sharpening results for a Suwannee Lime Cutter, made from blade stock of thickness 0.14 inches, which is twice as thick as the previous example. As in the previous sample, the WSKO-BGA was set to 15 degrees, so we should expect a nominal edge angle of 30 degrees:

For this thicker blade, the offset between the tool setting and what I measure as the inclusive apex angle is 6 degrees.

From these results, I conclude

• The convex profile of the edge formed by the WSKO-BGA calls for careful definition of, and control over, how the edge apex angle is measured.
  
  
• For a given tool configuration, different blade thicknesses will result in different edge apex angles.

I'm afraid this means there can be no simple answer to the question "To get an edge angle of X degrees, where do I set the tool?"

 

[jalapeno]

I've never seen this particular tool up close. Is there a backing plate behind the point of contact on the belt (like your typical bench-top 1" wide belt sander) that you have removed, or is there just not one in the first place? If there isn't one, what if you added one, to essentially set a stop on the peak belt flex? You could even offset the backing plate a quarter inch (or whatever) behind the static belt position if you wanted to preserve the convex grind to a controlled amount (and a hunk of HDPE would probably work for the backing plate just as well as an aluminum plate). It would be one less variable, is all I'm thinking.

 

[Cyrano]

... Is there a backing plate behind the point of contact on the belt (like your typical bench-top 1" wide belt sander) that you have removed, or is there just not one in the first place?

The tool has no plate behind the point of contact between the blade and the belt.

If there isn't one, what if you added one, to essentially set a stop on the peak belt flex? ...

If you believe my theoretical diagrams above, this won't make a difference. The thin blade case and the thick blade use exactly the same belt shape. The difference between the two cases is caused not by a difference in the curve of the belt, but by a difference in how much of that curve is replicated to the blade.

 

[cbwx34]

Well, 1.5-3 deg. per side, (vs. 8-10 deg. per side from the earlier posts), seems more in line with what I would expect, and am getting myself. It may be worth noting that the standard setup on the WSKO compensates a bit for belt flex, so if you set 20 deg. you're actually getting approx. 20 deg., even with the belt flex. The BGA makes no compensation... as my earlier picture showed... 20 deg. is approx. the angle between the two pulleys. So any flex will result in a higher angle. (The instructions recommend 1/16" belt flex).

I think you're right, it may be difficult to guarantee a specific angle, especially on a convex belt sharpener with no backing. But, I would venture you could "get in the ballpark" of where you want to be with more experience... and obviously if sharpening your own knives, notes (and a Sharpie) should help insure repeatability. If wanting to maintain the knife with another sharpener (Sharpmaker for example), I think most would use the WSKO-BGA at a lower angle, than the Sharpmaker to create/maintain a microbevel.

There is also a platen on the front of the BGA if you want a flat grind... (no angle settings there though, have to figure that out with some other method).

Nice work!

 

[HeavyHanded]

Theory proposes, experiment disposes. Let's start with theory:

Consider a thin blade having an edge apex angle of 37 degrees inclusive being sharpened in the WSKO-BGA. The blade is kept horizontal at 0 degrees, and the tool is set to a belt angle of 10 degrees, with the intent of achieving a new blade apex angle of 20 degrees inclusive.

Start with no contact between the blade and the belt:

Now bring the blade towards the belt, keeping the blade at 0 degrees, until the blade just contacts the belt. Contact will be made at the shoulder of the existing edge:

As the blade is pushed against the belt, the belt begins to flex:

As sharpening proceeds, steel is removed from the blade, and the sharpened region gets wider. This continues until the sharpened region hits the apex:

The blade is flipped over, and the sharpening process is repeated on the other side:

The final edge geometry has an angle of 15 degrees inclusive at the edge shoulder, and 24 degrees inclusive at the apex. The inclusive apex angle is 4 degrees greater than the intended target.

Now let's repeat this exercise for a thicker blade, with the same initial edge apex profile, and keeping the same 10-degree setting for the tool.

Start with no contact between the blade and the belt:

Now bring the blade towards the belt, keeping the blade at 0 degrees, until the blade just contacts the belt. Contact will be made at the shoulder of the existing edge:

As the blade is pushed against the belt, the belt begins to flex:

As sharpening proceeds, steel is removed from the blade, and the sharpened region gets wider. This continues until the sharpened region hits the apex:

The blade is flipped over, and the sharpening process is repeated on the other side:

The final edge geometry has an angle of 17 degrees inclusive at the edge shoulder, and 37 degrees inclusive at the apex. The inclusive apex angle is 17 degrees greater than the intended target.

So much for theory. Now, experiment disposes:

This sample shows my sharpening results for an Opinel no. 8, made from thin blade stock (0.07 inches thick.) The WSKO-BGA was set to 15 degrees, so we should expect a nominal edge angle of 30 degrees:

For this thin blade, the offset between the tool setting and what I measure as the inclusive apex angle is 3 degrees.

This sample shows my sharpening results for a Suwannee Lime Cutter, made from blade stock of thickness 0.14 inches, which is twice as thick as the previous example. As in the previous sample, the WSKO-BGA was set to 15 degrees, so we should expect a nominal edge angle of 30 degrees:

For this thicker blade, the offset between the tool setting and what I measure as the inclusive apex angle is 6 degrees.

From these results, I conclude

• The convex profile of the edge formed by the WSKO-BGA calls for careful definition of, and control over, how the edge apex angle is measured.
  
  
• For a given tool configuration, different blade thicknesses will result in different edge apex angles.

I'm afraid this means there can be no simple answer to the question "To get an edge angle of X degrees, where do I set the tool?"

Fascinating stuff, thanks for doing the work and included graphics.

Looking at this you could get a more accurate rough estimate and assume the target angle is midway between the shoulder and the apex. The real question is how much deflection can one expect from an average belt, but that will be all over the place also dependent to some extent on belt speed.

I run into this as well, as I sometimes use a belt to reset the bevel, and then transition to a hard stone for medium and fine work. Where to set my angle to minimize how much follow on work I need to do if I want all trace of the rougher scratch to be erased?

You'd think I would set the belt to a more acute angle, but in practice I find a slightly less acute or identical (as much as is practical) angle is better as I have to remove more steel to grind back up to the shoulder transition than the edge. Normally I stop short of creating a burr on the belt and this reduces overall blade width loss to about what it would have been if I'd done the whole thing on a flat stone.

 

[Mattysc42]

Today I sharpened my lc200n spyderco mule on the bga with the pulleys in the near position and the angle set to 15 degrees. I sold my we100 at the end of September and preordered the we50, which should supposedly be shipping to me in 'early November'. When that gets here I'll check the angle and let you guys know the results.

 

[Cyrano]

This is important:

Even with no variation in belt flex, nor in belt setting angle, nor in sharpening technique, blades of different geometries will result in different apex angles. ​

This is a consequence simply of geometry, as illustrated above. I see no way to get around this, other than eliminating flex from the belt.

But wait, there's more ...

Consider a thin blade having a primary grind angle of 17 degrees and an edge apex angle of 28 degrees inclusive being sharpened on the WSKO-BGA. The blade is kept horizontal at 0 degrees, and the tool is set to a belt angle of 10 degrees, with the intent of achieving a new blade apex angle of 20 degrees inclusive.

Start with no contact between the blade and the belt:

Now bring the blade towards the belt, keeping the blade at 0 degrees, until the blade just contacts the belt:

As the blade is pushed against the belt, the belt begins to flex:

As sharpening proceeds, steel is removed from the blade, and the sharpened region gets wider. This continues until the sharpened region hits the apex:

If we stopped here, as we did in previous examples, we'd end up with an apex angle of 28 degrees. We haven't changed the apex angle from its starting point; all we've done is thin the shoulder.

So let's not stop here. Let's keep going, sharpening past the point where we first hit the original apex:

Then we repeat this amount of sharpening on the other side:

The result is this final edge geometry:

The final edge geometry has an angle of 6 degrees inclusive at the edge shoulder, and 18 degrees inclusive at the apex. The inclusive apex angle is 2 degrees less than the intended target.

So, our important statement is expanded:

Even with no variation in belt flex, nor in belt setting angle, nor in sharpening technique, blades of different geometries will result in different apex angles. Resulting apex angles can range from less than the target tool setting to greater than the target tool setting. ​

If we could create a mathematical model of the actual shape of the flexed belt, this exercise could allow for useful prediction of results. I'm thinking of a spreadsheet:

• User inputs are: blade thickness, primary grind angle, initial apex angle, some measure of how far past the initial apex sharpening is to extend, and which belt is to be used. (The latter will be used in the internal programming of the spreadsheet to choose an appropriate equation to describe the shape of the flexed belt.)

• Outputs are: Shoulder angle, apex angle, width of sharpened edge. (The latter will be useful in predicting the aesthetic consequences of sharpening.)

Creating such a mathematical model of the shape of the flexed belt is beyond my capabilities. I expect it will require, for each type of belt, empirical data across a range of belt angles, belt tensions, and blade-to-belt pressures.​

 

[cbwx34]

I think you're making "belt flex" improperly fit your scenario.

In your first example, if the belt didn't flex at all, then when you reached the apex, you'd have a 10 deg. apex. But when you add the belt, you seem to flex the belt until you manage to thin the shoulder, but still maintain the 14 deg. (28 inclusive) angle at the apex. Not really how it works.

In the 2nd example, even if you ignore the error created by the first... what I see is a knife that has been totally reground... totally independent of any part of the original blade. None of your dotted lines (in the 2nd to the last picture), match with any part of the original blade. I think in theory, all you did was grind a new knife. That's what it looks like to me anyway.

 

[David45]

I think that’s the point. Don’t we use the belt system to regrind till we get a convex edge at whatever angle prefer?

 

[Cyrano]

... In your first example, if the belt didn't flex at all, then when you reached the apex, you'd have a 10 deg. apex. But when you add the belt, you seem to flex the belt until you manage to thin the shoulder, but still maintain the 14 deg. (28 inclusive) angle at the apex ...

In all these illustrations, I've used the same belt shape, which is simply a large ellipse. My assumptions are:

• The portion of the belt in use is flat until the blade makes contact.
• When the blade makes contact, it pushes the belt into the elliptical shape.
• The elliptical shape is unchanged during all subsequent sharpening.

I believe the last assumption to be reasonable, because I aim to keep a constant blade-to-belt pressure during sharpening.

In my most recent illustration, I followed the same procedure as in previous illustrations, as precisely as I could considering these are manual image manipulations. In that illustration, the fact that the apex angle was unchanged at the time sharpening hit the apex is simply luck; I did not cherry-pick dimensions or angles in order to make it work out this way.

... Not really how it works.

I don't profess to understand how such a complex system really works -- but I have experienced this phenomenon. On a knife with thick blade stock and an obtuse V-grind, I attempted to create a convex edge with a more acute apex angle. I knew this would require removing quite a bit of steel. What I did not expect was that after removing so much steel, I was left with an apex angle almost unchanged from before I started.

Factory edge profile:

Edge profile after reprofiling with WSKO-BGA set to 15 degrees, shown as a green outline over the image of the factory edge:

... what I see is a knife that has been totally reground... totally independent of any part of the original blade. None of your dotted lines (in the 2nd to the last picture), match with any part of the original blade. I think in theory, all you did was grind a new knife. That's what it looks like to me anyway.

This is an inescapable consequence of geometry. If you're starting with a planar V-grind, and you wish to form a more acute apex angle using any planar or concave sharpening surface, you will have to remove all of the original edge.

The only way around this is to use a convex sharpening surface.

 

[Cyrano]

I'd like to do a more thorough calibration for just one tool setting, like this:

Does anyone know of a source of inexpensive steel strips of these (or similar) thicknesses? I thought to get a feeler gauge set, but all those I've found max out way too thin.

 

[Cyrano]

I've found a source for my steel samples.

 

[HeavyHanded]

I'd expect some variation in amount of convexity/deflection based on belt speed as well. Slower speeds will tend to have more deflection at the same amount of applied force.

 

[Cyrano]

I'd expect some variation in amount of convexity/deflection based on belt speed as well. Slower speeds will tend to have more deflection at the same amount of applied force.

Agreed.

I'd wager there are a dozen other variables involved of which I'm unaware. Given the number of uncontrolled variables, I don't expect my study to provide quantitative predictive power for anyone but me.

I do hope that my results capture the effects of real physical mechanisms, and so could be qualitatively applicable to all users. If this proves true, then perhaps a user could combine my results with one or two data points of their own to create a personalized model which would have quantitative predictive power for them.